**Well Posedness and Finite Element Approximability of Three-Dimensional Time-Harmonic Electromagnetic Problems Involving Rotating Axisymmetric Objects**

### **Praveen Kalarickel Ramakrishnan † and Mirco Raffetto \*,†**

Department of Electrical, Electronic, Telecommunications Engineering and Naval Architecture,

University of Genoa, Via Opera Pia 11a, I–16145 Genoa, Italy; pravin.nitc@gmail.com

**\*** Correspondence: mirco.raffetto@unige.it; Tel.: +39-010-3352796

† These authors contributed equally to this work.

Received: 6 December 2019; Accepted: 19 January 2020; Published: 2 February 2020

**Abstract:** A set of sufficient conditions for the well posedness and the convergence of the finite element approximation of three-dimensional time-harmonic electromagnetic boundary value problems involving non-conducting rotating objects with stationary boundaries or bianisotropic media is provided for the first time to the best of authors' knowledge. It is shown that it is not difficult to check the validity of these conditions and that they hold true for broad classes of practically important problems which involve rotating or bianisotropic materials. All details of the applications of the theory are provided for electromagnetic problems involving rotating axisymmetric objects.

**Keywords:** electromagnetic scattering; time-harmonic electromagnetic fields; moving media; rotating axisymmetric objects; bianisotropic media; variational formulation; well posedness; finite element method; convergence of the approximation
